‎Mathematics‎

‎"DEDEKIND, VON R.‎

‎Ueber Gruppen, deren sämmtliche Theiler Normaltheiler sind. - [FIRST PRINTING OF DEDEKIND GROUP / HAMILTONIAN GROUP]‎

‎Leipzig, B.G. Teubner, 1897. 8vo. Original printed wrappers, no backstrip. In ""Mathematische Annalen. 48. Band. 4. Heft."" Entire issue offered. Minor soiling to back wrapper, internally fine and clean. [Dedekind:] Pp. 548-61. [Entire issue: 433-606, (2) pp.].‎

‎"DIRICHLET, G. LEJEUNE. - THE INTRODUCTION OF THE ""DIRICHLET SERIES""‎

‎Recherches sur diverses applications de L'Analyse infinitésimale à la Théorie des Nombres. Premiere - Seconde artie. (2 Papers).‎

‎Berlin, G. Reimer, 1839-40. 4to. Without wrappers. Extracted from: ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", Bd. 19 a. Bd. 21, pp. 324-369 a. pp. 1-12.. 4 leaves in part 1 with browning, due to the poor paperquality.‎

‎First appearance of this importent paper in which he introduces the ""Dirichlet series"", applicating analysis to the theory of numbers. The paper is especially known for its central use of the limiting proces.‎

Bookseller reference : 41972

‎"DIRICHLET, LEJEUNE (+) DEDEKIND.‎

‎Untersuchungen über ein Problem der Hydrodynamik [Dirichlet] (+) Zusatz zu der vorstehenden Abhandlung [Dedekind].‎

‎Berlin, Georg Reimer, 1861. 4to. As extracted from ""Journal für die reine und angewandte Mathematik, 1861, band 58. Without backstrip. Fine and clean. Pp. 181-228.‎

‎First printing of these two important papers on gravitational interaction from bodies, such pseudo-rigid bodies, thereby ""opened a new direction"", a direction which later inspired Riemann to turn his attention to the problem""Without the gravitational interaction from another body, such pseudo-rigid bodies havereceived attention in many references. The interest was initiated by Newton in Principia, where he showed that a spinning axi-symmetric self-gravitating body of ?uid that is rotating slowly about the symmetry axis will be oblate. Jacobi in 1834 extended the work of Newton, but also work of Maclaurin, to show that a self-gravitating ?uid also can take on ellipsoidal shapes. The solutions of Jacobi, Maclaurin and Newton were, however, still all rigid. In a frame rotating with the body the ?uid is stationary. Dirichlet and Dedekin, [in the present two papers], respectively, opened a new direction when they found a symmetry that applied to Jacobi's solution generated a new solution in which the body isstationary in shape but the ?uid particles follow elliptical paths in planes orthogonal to a principle axis of the ellipsoid. Dirichlet's paper inspired Riemann to turn his attention to the problem. He gave a classi?cation of the solutions of Dirichlet's equations for which the ellipsoidal shape of the body remains constant. At the heart of this classi?cation lies what is now known as Riemann's theorem: the angular velocity and circulation (i) lie in the same principle plane and (ii) if the angular velocity is parallel to a principle axis then the circulation vector must also lie along that same principle axis."" (Kristiansen, The two-body problem of a pseudo-rigid body and a rigid sphere)‎

Bookseller reference : 49315

‎"DIRICHLET, GUSTAV PETER LEJEUNE.‎

‎Solution d'une question relative à la théorie mathematique de la chaleur.‎

‎Berlin, G. Reimer, 1830. 4to. No wrappers. As extracted from ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle, 5. Band"". No backstrip. A fine and clean copy. 287-295 pp. [Entire issue: 287-318 pp].‎

‎"DUBISLAV, WALTER. - DEDICATION COPY.‎

‎Die Philosophie der Mathematik in der Gegenwart.‎

‎Berlin, Junker und Dünnhaupt, 1932. Lex8vo. Orig. printed wrappers. A small nick to frontwrapper at top of spine. Stamps on halftitle and foot of titlepage. VIII,88 pp. Inscribed from the author on halftitle (to Jørgen Jørgensen) ""Mit den besten Grüssen vom Verf./ übersandt"". From the library of the Danish logician and philosopher Jørgen Jørgensen with his name on frontwrapper.‎

‎First edition (Philosophische Forschungsberichte Heft 13).Dubislav was joint founder (with Hans Reichenbach and Kurt Grelling) of the 'Berlin Society for Empirical (later: Scientific) Philosophy' (Berliner Gesellschaft für empirische Philosophie), which, along with the Vienna Circle, is one of the points of origin of logical empiricism. The founding members of the Berlin Circle were listed as sympathisers within the Vienna Circle.Dubislav focused on a logical and mechanistic foundation of mathematics and physics, influenced by Bernard Bolzano's ""Theory of Science"" (Wissenschaftslehre). He presented a formalised account of Gottlob Frege's theory of definitions.‎

Bookseller reference : 48033

‎"EISENSTEIN, G.‎

‎Über die Irreductibilität und einige andere Eigenschaften der Gleichung, von welcher die Theilung der ganzen Lemniscate abhängt (+) Über eine allgemeine Eigenschaften der Gleichung, von welcher die Theilung der ganzen Lemniscate abhängt, nebst Anwendu... - [Eisenstein's Criterion]‎

‎Berlin, G. Reimer, 1850. 4to. Bound in later marbled wrappers, as extracted from ""Journal für die reine und angewandte Mathematik, 28 Band, 4. Heft, 1844"". Very fine and clean. Pp. 160-179" Pp. 224-274 Pp. 275-287 [Entire issue: 289-380 + 2 folded plates].‎

‎"EISENSTEIN, G. [GOTTHOLD].‎

‎Beiträge zur Theorie der elliptischen Functionen (+) Notiz über Partialbrüche‎

‎Berlin, G. Reimer, 1846. 4to. In ""Journal für die reine und angewandte Mathematik, 33 Band, 1. Heft, 1846"". In the original printed wrappers, without backstrip. Fine and clean. Last leaf with repair. [Eisenstein:] Pp. 59-70" " Pp. 71-88. [Entire issue: IV, 92, (2) + 2 plates.].‎

‎"EISENSTEIN, G. [GOTTHOLD].‎

‎Nachtrag zum cubischen Reciprocitätssatze für die aus dritten Wurzeln der Einheit zusammengesetzten complexen Zahlen. Criterien des cubischen Characters der Zahl 3 und ihrer Theiler (+) Transformations remarquables de quelques séries (+) La loi de réc... - [""THERE HAVE BEEN ONLY THREE EPOCH-MAKING MATHEMATICIANS: ARCHIMEDES, NEWTON, AND EISENSTEIN""]‎

‎Berlin, G. Reimer, 1844. 4to. In ""Journal für die reine und angewandte Mathematik, 28 Band, 1 Heft, 1844"". In the original printed wrappers, without backstrip. Fine and clean. [Eisenstein:] Pp. 28-35" Pp. 36-43 Pp. 44-48 Pp. 49-52 " Pp. 53-67. [Entire issue: IV, 96, (2) pp. + 2 folded plates.].‎

‎"ELFVING, GUSTAV.‎

‎Convex Sets in Statistics.‎

‎Lund, Håkan Ohlssons,1953. 8vo. In the original grey printed wrappers. Offprint from ""Comptes Rendu du Douzième Congrès des Mathématiciens Scandinaves tenu à Lund 10-15 août 1953"". A very fine clean copy, near mint. Pp. (2), 35-39.‎

‎Scare offprint of Elfving's important paper on ""Elfving sets"". Elfving are famous for having introduced optimality theory of regression theory.‎

Bookseller reference : 48791

‎"ELFVING, GUSTAV.‎

‎Zur theorie der markoffschen ketten.‎

‎Helsingfors, 1937. Royal8vo. In the original printed wrappers. Offprint from ""Acta Societatis Scientiarum Fennicæ"", Nova Series A. Tom. II, N:o 8. Wrappers partly detached and has been bended vertically. Internally fine. 17 pp.‎

‎Offprint of Elfving's paper on Markoff chains. Gustav Elfving known as one of the founders of the modern theory of the optimal design of experiments.‎

Bookseller reference : 48890

‎"ELFVING, GUSTAV.‎

‎Optimum allocation in linear regression theory. - [BEGINNING ""METHODS OF COMPUTING OPTIMUM REGRESSION DESIGN""]‎

‎U.S.A., The Annals of Mathematical Statistics, 1952. 8vo. No wrappers (as issued). Offprint from ""The Annals of Mathematical Statistics"", Vol. 23, No. 2, June 1952. Light miscolouring to extremities, otherwise a fine and clean copy. Pp. 255-262.‎

‎"ERICKSON, V. B. + J. F. PELLEGRIN.‎

‎Build - A Software Construction Tool. [In: AT&T Bell LaboratoriesTechnical Journal, July-August 1984, Vol. 63 No. 6 Part 2]. - [THE UNIX-BASED BUILD TOOL]‎

‎[N.Y., AT&T Bell Laboratories, 1984]. 8vo. In the original yellow wrappers. A nice and clean copy. Pp. 1049-1059 (Entire volume: 1 leaf + pp. 1007-1212).‎

‎First description of the UNIX-based Build tool.""The Build tool is used as a sophisticated method of generation and modifying software system. Build is being used successfully by a number of UNIX software-based projects at AT&T Bell Laboratories. [...] The Build tool is being used by a number of large software development projects as the primary software generation tool. Build plays a central role in the development strategies and standards used in these projects"". (From the introduction to the present article).""Unix is unquestionably the most influential operating system ever developed"" is has influenced virtually every subsequent operating system, including MS-DOS, Mac OS, Sun' Solaris, and many more"". (Pfaffenberger, Bryan. Linux clearly explained, 1999, p. 3).‎

Bookseller reference : 42729

‎"ERDMANN, BENNO.‎

‎Die Axiome der Geometrie. Eine philosophische Untersuchung der Riemann-Helmholtz'schen Raumtheorie.‎

‎Leipzig, Leopold Voss, 1877. Contemp. hcalf. Spine gilt and gilt lettering. Very lightly rubbed. X,174 pp. Internally fine and clean.‎

‎"EULER, LEONHARD. - THE GAME PHARON.‎

‎3 works by Euler: Nouvelle Méthode d'Éliminer les Quantités inconnues des Equations. - Recherches sur les Microscopes a´Trois Verres et les Moyens de les Perfectionner. - Sur L'Avantage du Banquier au Jeu du Pharaon.‎

‎(Berlin, Haude et Spener, 1766). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles Lettres"", tome XX, pp. 91-164 (91-116"117-143"144-164). 1 engraved plate ( belonging to ""Microscope..."")‎

‎3 first editions by Euler in algebra, in optics and in the theory of chance - in this last paper he discusses the so-called St. Petersburg paradox, the Game Pharon.‎

Bookseller reference : 31081

‎"EULER, LEONHARD - LOGARITHMS OF NEGATIVE NUMBERS.‎

‎De la Controverse entre Mrs. Leibnitz & Bernouilli sur les Logarithmes des Nombres Negatifs e Imaginaires. (Controversy between Mr Leibniz and Mr Bernouilli on the logarithms of negative and imaginary numbers).‎

‎(Berlin, Haude et Spener, 1751). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome V, pp. 139-179.‎

‎First edition of this importent paper on the logarithms of complex numbers, where Euler clarified such functions. He disagreed with Leibniz that a special function was only applicable for positive numbers, and showed that i was applicable for both negative and positive numbers, only with a difference of a constant. When Euler here (the offered item) came out with the correct form for the logarithm, it was not generally accepted. - Enestrom, Euler Bibliography E 168.‎

Bookseller reference : 36103

‎"EULER, LEONHARD.‎

‎De Minimis oscillationibus Corporum tam rigidorum qvam flexibilium. Methodus nova et facilis. (On the smallest oscillations of rigid and flexible bodies. A new and easy method.)‎

‎(Petropoli, St. Petersburg, Typis Academiae, 1740). 4to. No wrappers. In: ""Classes Prima continens Mathematica. Commentarii Academiae Scientiarum Imperialis Petropolitanae"", Tomus VII ad Annum 1735, &..... Euler's paper: pp. 99-122 a. 2 engraved plates. Wide-margined, clean.‎

‎First printing of Euler's first paper on vibrating bars. Euler here solves the partial differential equation for a forced harmonic oscillator and notices the resonnance phenomenon. - Enestroem E40.‎

Bookseller reference : 50924

‎"EUCLID (EUKLID) OF ALEXANDRIA.‎

‎Euclidis Megarensis mathematici clarissimi Elementorum geometricorum libri XV. Cum expositione Theonis in priores XIII à Bartholomæo Zamberto Veneto (= Zamberti) latinitate donata, Campani in omnes, & Hypsiclis Alexandrini in duos postremos. His addie...‎

‎Basel, Johannem Hervagium & Bernhardum Brand, 1558. Folio. (30,5x21,5). Bound in 19th century brown hmorocco with 5 raised bands. Light wear to back and corners a bit bumped. (2),587 pp.Numerous wood-cut diagrams and initials throughout. First ab. 20 leaves with different degrees of yellowing and occasional with marginal faint dampstaining. 3 leaves with upper right corners repaired without loss of text. The ""privilege"" at verso of title partly unreadable as a piece of paper is pasted on, some of these letters are faint, just as some letters in ""Basiliae"" on title are weak. Last leaf with colophon and printers large woodcut-device on verso is mounted, but not hiding the wood-cut. The word ""Basiliae"" on last leaf recto, is weak or nearly gone. Overall a large good copy as usually without the foreword by Melanchton. A small rubber-stamp on title: ""Duplum Bibliothecæ V.E."" and in old hand: ""Bibliothecæ Conventij Romani S. Andrea de Fratrij (?)""‎

‎Scarce third printing of the so-called Zambert-Campanus Edition of the Elements, all printed by Johann Herwagen in Basel - this edition printed together with his son-in-law Bernhard Brand. The first of the Herwagen prints was the famous Editio Princeps in Greek from 1533, and in 1537 he published a Latin version, which became the first Euclid-editon to contain also Euclids smaller tracts as ""Phenomena""(Spherical geometry), ""Katroptik"" (Mirror-reflexion), ""Optik"" und ""Data""(Geometrical excersises). The 1537- edition was reprinted 1546 and in 1558 (the present).""The most famous source of Greek geometry is the monumental work of Euclid of Alexandria, called the ""Elements"" (around 300 B.C.). No other book of science had a comparable influence on the intellectual development of mankind. It was a treatise of geometry in thirteen books which included all the fundamental results of scientific geometry up to his time. Euclid did not claim for himself any particular discovery, he was merely a compiler. Yet, in view of the systematic arrangement of the subject matter and the exact logical procedure followed, we cannot doubt that he himself provided a large body of specific formulations and specific auxiliary theorems in his deductions. It is no longer possible to pass judgement on the authorship of much of this material"" his book was meant as a textbook of geometry which paid attention to the material, while questions of priority did not enter the discussion."" (Cornelius Lanzos in ""Space through the Ages"").Max Steck III:57 - Thomas-Stanford: 15 - Riccardi 1558/3 - Adams E:976.‎

Bookseller reference : 32859

‎"EUCLID (EUKLID) OF ALEXANDRIA. - FIRST DANISH EDITION OF ""EUCLID"".‎

‎Euclidis Elementa Geometriæ, Det er, Første Grund Til Geometrien, I det Danske Sprog oversat af Ernst Gotlieb Ziegenbalg.‎

‎Kjøbenhavn, Ernst Henrik Berling, 1744. 4to. Samt. hldrbd. over træ. Ryg lidt slidt Overtrækspapiret på permer med mangler.(12),20,311 pp. samt 5 foldede kobberstukne plancher, i teksten talrige geometriske figurer. De første blade og de 5 plancher med en svag vandskjold. Svag skjold på de sidste ca 20 blade. En del blade med brunplet i øvre margin.4to. Contemporary half calf over wooden boards. Spine a bit worn and lacing some of the paper over boards. Faint damp stain to first leaves, to plates, and to the last ab. 20 leaves. Some leaves with a brown spot to upper margin. (12), 20, 311 pp + 5 folded engraved plates. Numerous geometrical figures in the text.‎

‎Første udgave på dansk af Euclids ""Elementer"", omfattende Bog 1-6 og 11-12. J.F. Ramus have allerede nogle år tidligere udgivet Euclid, men disse var mindre lærebøger i uddrag og på latin. Oversættelsen indeholder en lang introduktion af Ramus ""Betænkning om Euclidis Elementer og om deres Oversættelse i det Danske Sprog.""Ziegenbalg var teologisk kandidat, men havde studeret matematik i flere år, både i Jena og i England. Han blev udnævnt til professor i matematik ved Københavns Universitet efter Ramus, og havde i nogle år forinden fungeret som dennes assistent. Hans oversættelse er dedikeret Christian den VI, og i forordet introducerer han den således ""offereres (oversættelsen) Deres Kongelige Majestæt...disse udi det Danske Sprog oversatte Elementa Geometriæ, som ere Hoved=Kilden til alle Mathematiske Videnskaber og have nu i 2000 Aar været i saa stor Estime, at alle de største og erfarne Mathematici have grundet deres Skrifter paa dem og at de til almindelig Nytte og Brug ere bekientgiorte næsten udi alle Europæiske, men ey tilforn i dette Sprog.""First edition of the first Euclid-translation into Danish, comprising Book 1-6 and 11-12. Bound in cont. hcalf. Rebacked in old style. A good copy. - Riccardi, Bibl. Euclideana, Parte 4, p. 47. - Bibl. Danica IV:96.‎

Bookseller reference : 41890

‎"EULER, LEONHARD.‎

‎Exposition de quelques paradoxes dans le calcul integral.‎

‎(Berlin, Haude et Spener, 1758). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome XI, 1756 pp. 300-321 and 1 folded engraved plate.‎

‎First appearance of this paper in which Euler examines some peculiar differential equations that can be solved through the rather paradoxical method of integration by differentiation. He presents four such problems, which were found to all be members of the same family of differential equations, thus this presentation will focus on reworking several of these problems to make use of this generalization.Together with a paper by Eulers son (Euler le Fils - Johann Albrecht): Des Cerfs - Volans. Traduit du Latin. Pp. 322-364 and 3 folded engraved plates. - Johann here exposes his electrical theory in relation to kites, and indicates that kites were not only children's toys but had been used by the celebrated Romas in his electrical experiments.Enestroem E236.‎

Bookseller reference : 45702

‎"EULER, LEONHARD - THE PRINCIPLE OF LEAST ACTION‎

‎Harmonie entre les Principes generaux de repos et de Mouvement de M. de Maupertuis.‎

‎(Berlin, Haude et Spener, 1753). 4to. No wrappers, as extracted from ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome VII, pp. (167-)198.and 2 folded engraved plates.‎

‎First printing of this memoir in which Euler tries to show that the ""harmony"" between Maupertuis' Law of rest, which he formulated for any system of bodies attracted by forces, is a generalization of his own Principle of least Action.‎

Bookseller reference : 41693

‎"EULER, LEONHARD.‎

‎Principes de la Trigonometrie Spherique tirés de la Méthode des plus Grands et plus Petits (Principles of spherical Trigonometry deduced from the Method of Maxima and Minima). (And same author:) Élémens de la Trigonometrie spheroidique tirés de la Met... - [EULER'S SPHERICAL GEOMETRY]‎

‎(Berlin, Haude et Spener, 1755). 4to. Without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome IX, pp. 223-257 and 1 folded engraved plate (a tear to plate, no loss), and pp. 258-293 and 1 folded engraved plate.‎

‎Both papers first edition. The modern form of trigonometry as well of all trigonometry are due to Euler. Whereas trigonometry before Euler was concerned with trigonomic Lines, Euler's trigonometry deals with trigonomic Function. - ""In the first paper Euler constructs spherical trigonometry as the intrinsic geometry of the surface of the sphere. He expresses the line element ds of the surface in terms of the longitude and latitude of a point, defines the great circles as curves that minimize the integral of the line element, and, in connection with with the determination of the minimum of a side of a spherical triangle, derives 10 equations of spherical geometry.. After the discovery that the shape of the earth is that of a spheroid, Euler, (in the second paper here offered) extended his methods to spheroids. He develops this subject in its entirety...and here deduced very many of the formulas of spherical geometry"" (Rosenfeld & Abramovich). - Enestrom: E:214 a. E: 215. - Another Paper by Euler is withbound: Examen d'une Controverse sur la Loi de Refraction de Rayon de differentes Couleurs par Rapport a la diversité des Milieux transparens par lesquels ils sont transmis."" pp. 294-320. (Enestrom: E 216.‎

Bookseller reference : 39052

‎"EULER, LEONHARD.‎

‎Recherches sur le Mouvement de Rotation des Corps celestes (Studies on the rotational movement of celestial bodie). (And the same author:) Solution d'une Question curieuse qui ne paroit soumise a aucune Analyse. (Solutions of a curious question which ... - [RECREATIONAL MATHEMATICS]‎

‎(Berlin, aud et Spener, 1766). 4to. Without wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XV, pp. 265-309 a. 2 engraved plates., pp. 310-337.‎

‎Both papers first edition. In the first paper Euler uses his method of pertubations on, or the ""variation of the elements or parameters"" on the movement of the planets. - The second pper is one of Euler's more famous papers and a good example of his work in an area called ""recreational mathematics"". It was the first mathematical paper on knight's tours (A knight's tour is a path that a knight chesspiece can follow to visit every square on the chessboard without revisiting any square). (Eneroth: E 308 a. E 309).‎

Bookseller reference : 39047

‎"EULER, LEONHARD.‎

‎Recherches sur L'Origine des Forces.‎

‎(Berlin, Haude et Spener, 1752). 4to. Unbound, but stitched. In: ""Memoires de l'Academie Royale des Sciences et Belles-Lettres"" Tome VI, pp. (419-)447 and 1 folded engraved plate.‎

‎First edition, in the periodical form. - Enestroem No. 181.‎

Bookseller reference : 41244

‎"EULER, [LEONHARD].‎

‎Recherches sur la veritable courbe que decrivent les corps jettes dans l'air ou dans un autre fluide quelconque.‎

‎(Berlin, Haude et Spener, 1755). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome IX, pp. 321-352.‎

‎First printing of this Euler-paper in which he examines curves of airborne bodies. Euler describes how the forces acting on a cannonball give different differential equations for the ascending branch than for descending branch. See Eneström E217.‎

Bookseller reference : 44267

‎"EULER, [LEONHARD].‎

‎Reflexions sur un probleme de geometrie traite par quelques geometres et qui es neanmoins impossible (+) Recherches physiques sur la diverse refrangibilite des rayons de lumiere. - [EULER ON LIGHT RAYS]‎

‎(Berlin, Haude et Spener, 1756). 4to. No wrappers as issued in ""Memoires de l'Academie Royale des Sciences et Belles Lettres"". tome X, pp. 173-199" pp. 200-226.‎

‎First printing of two Euler-papers in which he occupies himself with an unsolvable geometric problem and the physics of the different refrangibilities of light rays, a field Euler made important and original contributions to. Euler's wave theory of light, published in 1746, was based on an analogy between sound and light to a more and more mathematical elaboration on that notion. His wave theory degenerated, and it was not until Fresnel introduced transverse waves and an elaborate notion of interference that the wave theory again progressed. He was the second after Christian Huygens to proposed a wave theory of light, and thereby one of the earliest to argue against Newton's particle theory of light. His 1740s papers on optics helped ensure that the wave theory of light proposed by Christian Huygens would become the dominant mode of thought until the development of the quantum theory of light.See Eneström E220, E221.‎

Bookseller reference : 44265